{"id":"aqua_rat:a8e586338e9e0bc4eac80809a03dfc99","source_id":"aqua_rat","source_item_id":"a8e586338e9e0bc4eac80809a03dfc99","external_id":null,"program":null,"section":"math","category_code":"PHM","category":"Preparing for Higher Math","subcategory_code":null,"subcategory":null,"form_id":null,"passage_id":null,"position":null,"scored":true,"layout_warning":null,"stem":"Let A, B and C denote the vertices of a triangle with area 10. Let point D be on side AB, point E be on side BC and point F be on side CA with AD = 2 and DB = 3. The area of △ABE and the area of quadrilateral DBEF are the same. What is the value of this area?","stimulus":"","stimulus_html":null,"stem_html":"<p>Let A, B and C denote the vertices of a triangle with area 10. Let point D be on side AB,</p><p>point E be on side BC and point F be on side CA with AD = 2 and DB = 3. The area of</p><p>△ABE and the area of quadrilateral DBEF are the same. What is the value of this area?</p>","rationale_html":"<p>First, note that 4AFD and 4AFE have the same area. Therefore, ED is parallel to AF.</p><p>Since 4DEB and 4ACB are similar, BE=EC = 3=2. Thus, the area of 4AEB is 3=5ths of the</p><p>area of 4ABC.</p><p>correct answer B</p>","correct_answer":["B"],"equiv_key":"d7333e340efbfc96fbc191a1","has_media":false,"has_mathml":false,"has_table":false,"section_label":"Mathematics","options":[{"label":"A","content_html":"<p>5.5</p>","ord":0},{"label":"B","content_html":"<p>6</p>","ord":1},{"label":"C","content_html":"<p>7</p>","ord":2},{"label":"D","content_html":"<p>8</p>","ord":3},{"label":"E","content_html":"<p>8.25</p>","ord":4}],"passage":null,"attribution":{"source_id":"aqua_rat","source_name":"AQuA-RAT algebra word problems with rationales","rights_holder":"Google DeepMind and the AQuA-RAT contributors","canonical_url":"https://github.com/google-deepmind/AQuA","retrieved_from":"https://raw.githubusercontent.com/google-deepmind/AQuA/master/","attribution":"Algebra word problems from the AQuA-RAT dataset (Ling et al., 2017), published by Google DeepMind under the Apache License 2.0.","disclaimer":"AQuA-RAT items are crowdsourced algebra problems, not ACT questions. They carry five answer choices in the pre-2025 ACT Mathematics style and no ACT reporting category. Useful for drilling Preparing for Higher Math content; not a substitute for a real form.","license":"Apache License 2.0. Crowdsourced by DeepMind and published for free use, including commercially.","redistributable":true,"item_count":508},"equivalents":[]}